It takes more than one season to see the effect of fatigue. Empirically, the SIM generates random statistical effects, this is why, for example, any given hitter performs at or below their real life performance, in combination, of course, with the effect of pitchers in any given league. The distribution of the SIM outcomes falls on a standard normal curve, and the distribution of hitting performances in any season does not necessarily reflect a normal distribution effect across all hitters or pitchers. This, of course, is also affected by the accuracy of the simulation in the first place. Along with the SIM effect, the fatigue effect will also have a normal curve and random distribution effect. Thus, the effect for any given league is an interaction of the normalcy in the distribution of players, the SIM effect, and the fatigue effect, all of which have variation components. Given the range of variations in all three of these components, a sample size greater than one is required. This would not be true if the parameters of the variables could be set and were invariant.

You can't control for the variation in the SIM. You would need the SIM itself to be set up to EXACTLY replicate the real life production of players. Only then could you say that the variation in the outcome is due to fatigue.

Posted by radlynch on 10/19/2013 11:07:00 PM (view original):You can't control for the variation in the SIM. You would need the SIM itself to be set up to EXACTLY replicate the real life production of players. Only then could you say that the variation in the outcome is due to fatigue.

There's variation in the SIM. Its part of how simulations work. Here's an example, one of the leagues I played, 12 of 16 teams used Addie Joss, 1908. He didn't perform identically for every team, which IN PART is a result of the composition of the team he is on and the teams he faces, and the stadiums, etc.,. But even without those factors, the SIM is based on an approximation of real life play. If it wasn't, then you wouldn't even need to play the league, because you could predict the results entirely from the draft.

The outcome of any simulation is based on mathematical probabilities. Those probabilities are distributed as a normal curve. A large number of simulation produces a normal curve; any particular simulation, however, can fall anywhere within the parameters of the normal curve, and may not represent an average outcome. This means that you need a certain number of runs of the SIM to generate the entire range of the curve to determine the mean effect.

In the SIM, even the fatigue affect will be randomly distributed -- its constructed the same way for all the players experiencing fatigue, BUT, the fatigue effect will be random for each particular at bat either from the pitcher's or the hitter's perspective. Its the sum of all the at bats that generates the normal distribution of the fatigue effect in any particular league under the conditions in the league.

As noted in previous posts, perhaps the best way to determine this effect is through the experimental design. But, this would still require a number of experimental design permutations and cross-referencing of the design outcomes. One design would be for every team to be the same and to play in the same stadium and to have the same batting order, pitching rotations and all the same advanced settings and managerial settings. In that case, you would have 16 players at each position to compare who are all the same, and with 16 cases you would come closer to getting an approximation of a normal curve than if you had one case. Statistically, there is a minimum number of cases you would need to ensure that you replicated the normal curve of any distribution to allow you to generalize from the results.

In the SIM, you can control some level of the variability, but not directly, by playing all the games in neutral parks. But, the neutral effect of parks is an estimation based on a normal distribution, and the outcome of every at bat isn't 0 -- the sum of the at bats in the park over the entire season should, if the SIM acts correctly, be 0. But, since the SIM is based on probability and a normal distribution, there is always the chance that the outcome isn't exactly 0. Mathematically, the SIM has a variation, a standard deviation, and a confidence interval, and given enough cases, these can be replicated, But with one SIM, you don't know if you replicate the mean and the distribution.

Question: i've read alot in the forums about fatigue and how to best use the full extent of your players to get the most bang for your buck. that being said it seems that 30 or 40% of the teams in the 60mil league have less than 1300 innings i dont understand how they can be competitive. wont there pitchers fatigue run down into the 80's and therefore hurt there teams abilities?, or are there players who perform better fatigued? and i should pay attention and learn. conversely 5 or 6 teams are starting under 5000 PA's and i feel are doing the same thing. are these guys going to "throw" for lack of a better word games with multiple AAA players in hopes that they can go 95-45 with their starters and then finish 102-60 and still make the playoffs.

My response (Sadly, the fatigue issue still awaits fixing): Well, I hate to say it, but it looks like several teams are going to use the "Fatigue Strategy" where they abuse certainly players to throw games to keep a core of players fresh enough to try to win 2/3 of their games. I HATE THIS STRATEGY!

Here's the way it works: You automatically get a free 10% fatigue cushion built in by WIS. So if you draft a guy with 500 PAs, he can get to 550 PAs and still be at 100%. Most people agree that the fatigue system really only hurts marginally up to 92%, so you get an extra 7% PAs until you start seeing diminishing stats. So your at 589 PAs now while only drafting 500.

The same thing works for pitchers, who fatigue on a number of pitches basis (not IP) and WIS uses a formula that is close to IP x 15.5 to calculate total pitches (or something like that). But you also get a free 10% bump in that number too, so if your pitchers throws 200 IP, you get 3100 pitches and really 3,410 with that factored in. The same 92% seems to be the cutoff for fatigue with pitchers too, so you add the 7% to get around 3,650/15.5 = 235 IP while only drafting 200.

I think this is crap, but many people game the system and do this.

Now, this league has AAA players, and even though they are "below average" they are very useful to prevent fatigue. From the AAA charts thread (http://www.whatifsports.com/forums/Posts.aspx?TopicID=388184), you find out that for position players, the lowest stamina you can get is F, which is still 150-300 PAs. I got a C at 1B which is 400-450 PAs! 6 x 150 = 900 PAs and I would guess that the average is around 1200 free PAs with the use of AAA guys. Pitchers are a bit more tricky because the salaries for Below average are only 200K - 949,999, so it's harder to get a lot of extra IP, but you get a minimum of 50 IP.

So, when you add in the fact that you can cheat the fatigue system and are getting nearly 1200 PAs (and remember, they get the bonuses too, so its really over 1,400) and a minimum of 50 IP, then a lot of guys draft really low PAs and IP and play the fatigue system thinking that they are drafting the highest quality stats and riding out the freebie PAs/IP.

There are supposedly some players who perform better fatigued (some owners have posted that OBP is not affected by fatigue and just4me has a great thread showing that low BB/9# pitchers are less affected by it) but some people just think that if you draft a guy who hits .300 and he plays at 80%, that's still better than drafting a guy who hits .250 and plays at 100%.

Frankly, I think it sucks and that's why I don't play in leagues with AAA typically. But I love low cap leagues and the challenge of making the best team you can with the players who are not all stars. It just appeals to me.

That said, I only drafted 4467 PAs and 1288 IP. But I knew I was getting 1200 PAs and likely 80 IP from AAA, so that's more like 5667 PAs and 1368 IP. It's likely going to be tough to keep my guys at 100%, but I should be able to do it with good managing.

So even though I am light on PAs (and will have to start a lot of different lineups), I should be able to keep my guys at 100%, and my AAA guys are descent (all of them hit at least .220 and some hit over .250), so I may be able to play them and hit them 6, 7, 8 when I need to rest guys.

That's going to be my plan...it's not throwing games (which I hate), it's realistic baseball to me where you have to guess when to rest your hitters and such and still try to win.

Does that help? Like I said in the forum post, if this league wouldn't have had access to AAA (and essentially a 33 man roster), I would have drafted 100% differently.